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Problem of the Week 808

How Many Isosceles Triangles?

Continuing with the tetrahedral theme, observe that the 4 vertices of a regular tetrahedron are such that every three of them form an equilateral triangle. How many points in 3-space can you find so that every three of them form an isosceles triangle? (Note: An equilateral triangle counts as isosceles.)

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998